The finite difference method for the three- dimensional nonlinear coupled system of dynamics of fluids in porous media

摘要

For the three-dimensional coupled system of multilayer dynamics of fluids in porous media, the second-order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in l~2 norm are derived to determine the error in the second-order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources.